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104 LearnersLast updated on September 24, 2025
GCF of 648 and 1029
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 648 and 1029.
What is the GCF of 648 and 1029?
The greatest common factor of 648 and 1029 is 81. The largest divisor of two or more numbers is called the GCF of the number.
If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 648 and 1029?
To find the GCF of 648 and 1029, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 648 and 1029 by Using Listing of Factors
Steps to find the GCF of 648 and 1029 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 648 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648. Factors of 1029 = 1, 3, 9, 19, 27, 57, 171, 343, 1029.
Step 2: Now, identify the common factors of them Common factors of 648 and 1029: 1, 3, 9, 27, 81.
Step 3: Choose the largest factor The largest factor that both numbers have is 81. The GCF of 648 and 1029 is 81.
GCF of 648 and 1029 Using Prime Factorization
To find the GCF of 648 and 1029 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 648: 648 = 2 x 2 x 2 x 3 x 3 x 3 x 3 = 2^3 x 3^4 Prime Factors of 1029: 1029 = 3 x 3 x 3 x 19 = 3^3 x 19
Step 2: Now, identify the common prime factors The common prime factors are: 3 x 3 x 3 = 3^3
Step 3: Multiply the common prime factors 3^3 = 27. The Greatest Common Factor of 648 and 1029 is 81.
GCF of 648 and 1029 Using Division Method or Euclidean Algorithm Method
Find the GCF of 648 and 1029 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 1029 by 648 1029 ÷ 648 = 1 (quotient), The remainder is calculated as 1029 − (648×1) = 381 The remainder is 381, not zero, so continue the process
Step 2: Now divide the previous divisor (648) by the previous remainder (381) Divide 648 by 381 648 ÷ 381 = 1 (quotient), remainder = 648 − (381×1) = 267
Step 3: Continue the process by dividing 381 by 267 381 ÷ 267 = 1 (quotient), remainder = 381 − (267×1) = 114 Finally, divide 267 by 114 267 ÷ 114 = 2 (quotient), remainder = 267 − (114×2) = 39 Then divide 114 by 39 114 ÷ 39 = 2 (quotient), remainder = 114 − (39×2) = 36
Finally, divide 39 by 36 39 ÷ 36 = 1 (quotient), remainder = 39 − (36×1) = 3 Then divide 36 by 3 36 ÷ 3 = 12 (quotient), remainder = 0 The remainder is zero, the divisor will become the GCF. The GCF of 648 and 1029 is 81.
Common Mistakes and How to Avoid Them in GCF of 648 and 1029
Finding the GCF of 648 and 1029 may seem straightforward, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 648, students may mention numbers that are not factors. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers.
Although it does not affect the GCF, it indicates an incomplete understanding of factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with multiples. In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 648 and 1029 Examples
Problem 1
A chef has 648 grams of flour and 1029 grams of sugar. She wants to divide them into equal portions using the largest possible weight. How many grams will each portion weigh?
We should find the GCF of 648 and 1029 GCF of 648 and 1029 3^3 = 27. There are 81 equal portions. 648 ÷ 81 = 8 1029 ÷ 81 = 12 There will be 81 portions, and each portion weighs 8 grams of flour and 12 grams of sugar.
Explanation
As the GCF of 648 and 1029 is 81, the chef can make 81 portions.
Now divide 648 and 1029 by 81.
Each portion contains 8 grams of flour and 12 grams of sugar.
Problem 2
A gardener has 648 tulip bulbs and 1029 daffodil bulbs. He wants to plant them in rows with the same number of bulbs in each row, using the largest possible number of bulbs per row. How many bulbs will be in each row?
GCF of 648 and 1029 3^3 = 27. So each row will have 81 bulbs.
Explanation
There are 648 tulip bulbs and 1029 daffodil bulbs.
To find the total number of bulbs in each row, we should find the GCF of 648 and 1029.
There will be 81 bulbs in each row.
Problem 3
A textile company has 648 meters of cotton fabric and 1029 meters of wool fabric. They want to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 648 and 1029 The GCF of 648 and 1029 3^3 = 27. The fabric is 81 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 648 and 1029, which is 81.
The length of each piece of the fabric will be 81 meters.
Problem 4
A carpenter has two wooden planks, one 648 cm long and the other 1029 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 648 and 1029 3^3 = 27. The longest length of each piece is 81 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 648 cm and 1029 cm, respectively, we have to find the GCF of 648 and 1029, which is 81 cm.
The longest length of each piece is 81 cm.
Problem 5
If the GCF of 648 and ‘b’ is 81, and the LCM is 7920. Find ‘b’.
The value of ‘b’ is 1029.
Explanation
GCF x LCM = product of the numbers
81 × 7920 = 648 × b
641520 = 648b
b = 641520 ÷ 648
= 1029
FAQs on the Greatest Common Factor of 648 and 1029
1.What is the LCM of 648 and 1029?
2.Is 648 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 1029?
5.Are 648 and 1029 prime numbers?
Important Glossaries for GCF of 648 and 1029
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 81 are 1, 3, 9, 27, and 81.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 9 are 9, 18, 27, etc.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 8 is 24.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
